两类集优化问题的Hadamard适定性研究

程翔; 彭再云; 杨鑫; 文铭

doi:10.21656/1000-0887.450273

两类集优化问题的Hadamard适定性研究

doi: 10.21656/1000-0887.450273

重庆交通大学数学与统计学院, 重庆 400074

基金项目:

国家自然科学基金(面上项目) 12271067

重庆市自然科学基金面上项目 CSTB2024NSCQ-MSX0973

重庆市教委科技研究项目重点项目 KJZD-202200704

重庆市高等教育教学改革研究项目重点项目 232072

重庆市研究生教育教学改革项目 yjg223094

教育部协同育人项目 220503414180513

详细信息

作者简介:
程翔(1999—), 女, 硕士生(E-mail: chengxiang9599@163.com)

通讯作者:
彭再云(1980—), 男, 教授, 博士, 博士生导师(通讯作者. E-mail: pengzaiyun@126.com)

中图分类号: O224
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- 被引次数: 0
出版历程
- 收稿日期: 2024-10-15
- 修回日期: 2025-06-08
- 网络出版日期: 2025-07-30
- 刊出日期: 2025-07-01

Hadamard Well-Posedness in 2 Types of Set Optimization Problems

School of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, P.R.China

摘要

摘要: 该文主要研究上序关系下集优化问题(P)和无限集优化问题(ISOP)的Hadamard适定性. 首先, 在集值映射序列Gamma-收敛的情形下, 给出了问题(P)的广义Hadamard适定性和ε-广义Hadamard适定性的概念, 讨论了这两类适定性之间的关系, 得到了问题(P)的Hadamard适定性的充分条件. 然后, 在约束集和目标函数都扰动的情形下, 利用Hausdorff-锥连续性研究了问题(ISOP)的Hadamard适定性的充分条件. 所得的结果改进了相关文献, 丰富了集优化问题的研究.
- 集优化问题 /
- Hadamard适定性 /
- Gamma-收敛 /
- Hausdorff-锥连续
Abstract: The Hadamard well-posedness of a set optimization problem (P) and an infinite set optimization problem (ISOP) under upper set order relation was studied. Firstly, in the case of the gamma convergence of the set-valued mapping sequence, the definitions of the generalized Hadamard well-posedness and the ε-generalized Hadamard well-posedness for (P) were given, the relationship between these 2 types of well-posednesses were established, and the sufficient conditions for the Hadamard well-posedness of (P) were obtained. Then the sufficient conditions for the Hadamard well-posedness of (ISOP) were studied with the concept of Hausdorff cone-continuity under functional perturbations of both constraint sets and objective maps. The results improve those in the relevant previous references, enriching the study of set optimization problems.
- set optimization problem /
- Hadamard well-posedness /
- Gamma-convergence /
- Hausdorff cone-continuity

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图 1 F的图像

Figure 1. The image of F

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图 2 F(x₀)-int C-εe的图像

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Figure 3. The image of F

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图 4 F_n的图像

Figure 4. The image of F_n

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